Three-Dimensional Nonlinear Finite Element Modeling of Mammalian Cornea to Study Mechanics of Spiraling

The cornea is a transparent tissue in front of the eye that refracts the light and makes vision possible. A slight change in the geometry of cornea remarkably affects the optical power. Biomechanical study of cornea can reveal much about its performance and function. Numerical techniques such as the finite element method (FEM) have been extensively implemented as effective and non-invasive methods for analyzing corneal mechanics and possible disorders. The focus of this dissertation is to use finite element analysis for studying biomechanical behavior of the cornea. This work also allows reviewing different applications of FEM in studying corneal diseases, surgery predictions, impact simulations and clinical applications. In some mammalian corneas such as mice and rats, the epithelial cells assort themselves into patterns that resemble spirals. The patterned arrangement of the corneal epithelial cells implies existence of some global processes or forces. However, a definitive explanation of the cause of these spiral patterns has not been determined. Studying the generation of these patterns is important as it may lead to greater understanding of corneal development and possible disorders. We propose here that the stresses and strains on the cornea surface facilitate sliding of epithelial cells into spiral patterns. In this dissertation, a framework for explaining the generation of this poorly understood phenomenon is presented. To this end, a finite element computer code is developed to perform three-dimensional and large deformation modeling of mammalian cornea. The cornea model includes the effect of preferentially oriented and dispersed collagen fibrils embedded in nearly incompressible matrix. The deformation, stresses and strain distribution in the cornea subjected to pressure (intraocular pressure) is investigated. An algorithm is devised to track the pathlines of critical strain directions that tend to form spiral pattern. These patterns are finally matched with logarithmic spirals obtained from confocal images of the rat cornea. We conclude that the mechanical behavior of the cornea may cause the observed spiral patterns.